"""Numpy based computation backend."""
import math
import numpy as np
from numpy import (
abs,
all,
allclose,
amax,
amin,
angle,
any,
arange,
arccos,
arccosh,
arcsin,
arctan2,
arctanh,
argmax,
argmin,
array,
broadcast_arrays,
broadcast_to,
ceil,
clip,
concatenate,
conj,
cos,
cosh,
cross,
cumprod,
cumsum,
diag_indices,
diagonal,
divide,
dot,
)
from numpy import dtype as ndtype # NOQA
from numpy import (
einsum,
empty,
empty_like,
equal,
exp,
expand_dims,
eye,
flip,
float32,
float64,
floor,
greater,
hsplit,
hstack,
imag,
int32,
int64,
isclose,
isnan,
kron,
less,
less_equal,
linspace,
log,
logical_and,
logical_or,
matmul,
maximum,
mean,
meshgrid,
minimum,
mod,
moveaxis,
ones,
ones_like,
outer,
pad,
power,
prod,
real,
repeat,
reshape,
searchsorted,
shape,
sign,
sin,
sinh,
sort,
split,
sqrt,
squeeze,
stack,
std,
sum,
take,
tan,
tanh,
tile,
trace,
transpose,
trapz,
tril,
tril_indices,
triu,
triu_indices,
uint8,
unique,
vstack,
where,
zeros,
zeros_like,
)
from scipy.sparse import coo_matrix # NOQA
from scipy.special import erf, polygamma # NOQA
from ..constants import np_atol, np_rtol
from . import autodiff # NOQA
from . import linalg # NOQA
from . import random # NOQA
from .common import to_ndarray # NOQA
DTYPES = {
ndtype("int32"): 0,
ndtype("int64"): 1,
ndtype("float32"): 2,
ndtype("float64"): 3,
ndtype("complex64"): 4,
ndtype("complex128"): 5,
}
atol = np_atol
rtol = np_rtol
def comb(n, k):
return math.factorial(n) // math.factorial(k) // math.factorial(n - k)
def to_numpy(x):
return x
def from_numpy(x):
return x
def convert_to_wider_dtype(tensor_list):
dtype_list = [DTYPES[x.dtype] for x in tensor_list]
wider_dtype_index = max(dtype_list)
wider_dtype = list(DTYPES.keys())[wider_dtype_index]
tensor_list = [cast(x, dtype=wider_dtype) for x in tensor_list]
return tensor_list
def flatten(x):
return x.flatten()
def one_hot(labels, num_classes):
return np.eye(num_classes, dtype=np.dtype("uint8"))[labels]
[docs]def get_mask_i_float(i, n):
"""Create a 1D array of zeros with one element at one, with floating type.
Parameters
----------
i : int
Index of the non-zero element.
n: n
Length of the created array.
Returns
-------
mask_i_float : array-like, shape=[n,]
1D array of zeros except at index i, where it is one
"""
range_n = arange(n)
i_float = cast(array([i]), int32)[0]
mask_i = equal(range_n, i_float)
mask_i_float = cast(mask_i, float32)
return mask_i_float
def _is_boolean(x):
if isinstance(x, bool):
return True
if isinstance(x, (tuple, list)):
return _is_boolean(x[0])
if isinstance(x, np.ndarray):
return x.dtype == bool
return False
def _is_iterable(x):
if isinstance(x, (list, tuple)):
return True
if isinstance(x, np.ndarray):
return ndim(x) > 0
return False
[docs]def assignment(x, values, indices, axis=0):
"""Assign values at given indices of an array.
Parameters
----------
x: array-like, shape=[dim]
Initial array.
values: {float, list(float)}
Value or list of values to be assigned.
indices: {int, tuple, list(int), list(tuple)}
Single int or tuple, or list of ints or tuples of indices where value
is assigned.
If the length of the tuples is shorter than ndim(x), values are
assigned to each copy along axis.
axis: int, optional
Axis along which values are assigned, if vectorized.
Returns
-------
x_new : array-like, shape=[dim]
Copy of x with the values assigned at the given indices.
Notes
-----
If a single value is provided, it is assigned at all the indices.
If a list is given, it must have the same length as indices.
"""
x_new = copy(x)
use_vectorization = hasattr(indices, "__len__") and len(indices) < ndim(x)
if _is_boolean(indices):
x_new[indices] = values
return x_new
zip_indices = _is_iterable(indices) and _is_iterable(indices[0])
len_indices = len(indices) if _is_iterable(indices) else 1
if zip_indices:
indices = tuple(zip(*indices))
if not use_vectorization:
if not zip_indices:
len_indices = len(indices) if _is_iterable(indices) else 1
len_values = len(values) if _is_iterable(values) else 1
if len_values > 1 and len_values != len_indices:
raise ValueError("Either one value or as many values as indices")
x_new[indices] = values
else:
indices = tuple(list(indices[:axis]) + [slice(None)] + list(indices[axis:]))
x_new[indices] = values
return x_new
[docs]def assignment_by_sum(x, values, indices, axis=0):
"""Add values at given indices of an array.
Parameters
----------
x : array-like, shape=[dim]
Initial array.
values : {float, list(float)}
Value or list of values to be assigned.
indices : {int, tuple, list(int), list(tuple)}
Single int or tuple, or list of ints or tuples of indices where value
is assigned.
If the length of the tuples is shorter than ndim(x), values are
assigned to each copy along axis.
axis: int, optional
Axis along which values are assigned, if vectorized.
Returns
-------
x_new : array-like, shape=[dim]
Copy of x with the values assigned at the given indices.
Notes
-----
If a single value is provided, it is assigned at all the indices.
If a list is given, it must have the same length as indices.
"""
x_new = copy(x)
use_vectorization = hasattr(indices, "__len__") and len(indices) < ndim(x)
if _is_boolean(indices):
x_new[indices] += values
return x_new
zip_indices = _is_iterable(indices) and _is_iterable(indices[0])
if zip_indices:
indices = tuple(zip(*indices))
if not use_vectorization:
len_indices = len(indices) if _is_iterable(indices) else 1
len_values = len(values) if _is_iterable(values) else 1
if len_values > 1 and len_values != len_indices:
raise ValueError("Either one value or as many values as indices")
x_new[indices] += values
else:
indices = tuple(list(indices[:axis]) + [slice(None)] + list(indices[axis:]))
x_new[indices] += values
return x_new
[docs]def get_slice(x, indices):
"""Return a slice of an array, following Numpy's style.
Parameters
----------
x : array-like, shape=[dim]
Initial array.
indices : iterable(iterable(int))
Indices which are kept along each axis, starting from 0.
Returns
-------
slice : array-like
Slice of x given by indices.
Notes
-----
This follows Numpy's convention: indices are grouped by axis.
Examples
--------
>>> a = np.array(range(30)).reshape(3,10)
>>> get_slice(a, ((0, 2), (8, 9)))
array([8, 29])
"""
return x[indices]
def vectorize(x, pyfunc, multiple_args=False, signature=None, **kwargs):
if multiple_args:
return np.vectorize(pyfunc, signature=signature)(*x)
return np.vectorize(pyfunc, signature=signature)(x)
def cast(x, dtype):
return x.astype(dtype)
[docs]def set_diag(x, new_diag):
"""Set the diagonal along the last two axis.
Parameters
----------
x : array-like, shape=[dim]
Initial array.
new_diag : array-like, shape=[dim[-2]]
Values to set on the diagonal.
Returns
-------
None
Notes
-----
This mimics tensorflow.linalg.set_diag(x, new_diag), when new_diag is a
1-D array, but modifies x instead of creating a copy.
"""
arr_shape = x.shape
x[..., range(arr_shape[-2]), range(arr_shape[-1])] = new_diag
return x
def ndim(x):
return x.ndim
def copy(x):
return x.copy()
[docs]def array_from_sparse(indices, data, target_shape):
"""Create an array of given shape, with values at specific indices.
The rest of the array will be filled with zeros.
Parameters
----------
indices : iterable(tuple(int))
Index of each element which will be assigned a specific value.
data : iterable(scalar)
Value associated at each index.
target_shape : tuple(int)
Shape of the output array.
Returns
-------
a : array, shape=target_shape
Array of zeros with specified values assigned to specified indices.
"""
return array(coo_matrix((data, list(zip(*indices))), target_shape).todense())
[docs]def vec_to_diag(vec):
"""Convert vector to diagonal matrix."""
d = vec.shape[-1]
return np.squeeze(vec[..., None, :] * np.eye(d)[None, :, :])
def tril_to_vec(x, k=0):
n = x.shape[-1]
rows, cols = tril_indices(n, k=k)
return x[..., rows, cols]
def triu_to_vec(x, k=0):
n = x.shape[-1]
rows, cols = triu_indices(n, k=k)
return x[..., rows, cols]
[docs]def mat_from_diag_triu_tril(diag, tri_upp, tri_low):
"""Build matrix from given components.
Forms a matrix from diagonal, strictly upper triangular and
strictly lower traingular parts.
Parameters
----------
diag : array_like, shape=[..., n]
tri_upp : array_like, shape=[..., (n * (n - 1)) / 2]
tri_low : array_like, shape=[..., (n * (n - 1)) / 2]
Returns
-------
mat : array_like, shape=[..., n, n]
"""
n = diag.shape[-1]
(i,) = np.diag_indices(n, ndim=1)
j, k = np.triu_indices(n, k=1)
mat = np.zeros(diag.shape + (n,))
mat[..., i, i] = diag
mat[..., j, k] = tri_upp
mat[..., k, j] = tri_low
return mat
def ravel_tril_indices(n, k=0, m=None):
if m is None:
size = (n, n)
else:
size = (n, m)
idxs = np.tril_indices(n, k, m)
return np.ravel_multi_index(idxs, size)